Answer
$\frac{2xe^{x^2}}{\sqrt {e^{x^2}}}$
Work Step by Step
$y=\int_{0}^{e^{x^2}} ({\frac{1}{\sqrt t}dt}) =\int_{0}^{e^{x^2}} (t^{-1/2}dt) =[2\sqrt t]_{0}^{e^{x^2}}=[2\sqrt {e^{x^2}}]$ Let's differentiate this! $\frac{dy}{dx}=2\cdot\frac{1}{2}({e^{x^2}})^{-1/2}\cdot(2xe^{x^2})=\frac{2xe^{x^2}}{\sqrt {e^{x^2}}}$
